are two vector expression a⋅b=√P2−4‌tan‌A+P‌tan‌B+√P2+4‌tan‌C |a||b|cos‌θ=6P, where Q is the angle between a and b
‌√P2−4+P2+P2+4√tan2A+tan2B+tan2C
‌cos‌θ=6P ‌√3P√tan2A+tan2B+tan2C=6Psecθ Squaring both sides, 3[tan2A+tan2B+tan2C]=36sec2θ ⇒tan2A+tan2B+tan2C=12sec2θ As we know that sec2θ≥1,12sec2θ≥12 ‌tan2A+tan2B+tan2C≥12 ∴ Minimum value of ‌tan2A+tan2B+tan2C=12